Hot spots in near-field optics

We investigate the critical points of the near field intensity. It is shown that there are no local maxima of the intensity outside dielectric surfaces and the only possible critical points are either local minima or saddle points. Using the boundary charge method we investigate numerically the field distribution around star-like sets of prolate spheroids. The field enhancement is shown to achieve a value of several hundreds at critical points outside the surfaces of spheroids and of several thousands near the surfaces.